The problem is defined on the interval [tex]x_0 \leq x \leq x_1[/tex], where [tex]f\left(x,x',t\right)[/tex] is a known function. We have the initial condition [tex]A\left(x,0\right) = g\left(x\right)[/tex].

For my specific problem I found the qualitative behavior of the solution [tex]A\left(x,t\right)[/tex] by straightforward numerical integration. But I would like to be able to find analytic solutions... Any suggestions on how to proceed here?
Any help is very much appreciated!!